The Insurance Value of Medical...
Transcript of The Insurance Value of Medical...
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The Insurance Value of Medical Innovation*
Darius Lakdawalla
University of Southern California and NBER
Anup Malani
University of Chicago and NBER
Julian Reif
University of Illinois at Urbana‐Champaign
Abstract: Economists think of medical innovation as a valuable but risky good, producing health benefits
but increasing financial risk for consumers and healthcare payers. This perspective overlooks how
innovation can lower physical risks borne by healthy patients facing the prospect of future disease. We
present an alternative framework that accounts for all these sources of value and links them to the
value of healthcare insurance. We show that any innovation worth buying reduces overall risk and
generates positive insurance value on its own. We conduct a stylized numerical exercise to assess the
potential empirical significance of our insights. Our calculations suggest that conventional methods
meaningfully understate the value of historical health gains and disproportionately undervalue
treatments for the most severe illnesses, where physical risk to consumers is the costliest. These
calculations also suggest that the value of physical insurance from new technologies may exceed the
financial spending risk that they pose.
Key words: cost‐benefit analysis, health insurance, medical innovation, value of health
JEL codes: I13, I18, J17, O30
* We are grateful to Jeff Brown, Marika Cabral, Amitabh Chandra, Tatyana Deryugina, Don Fullerton, Gautam
Gowrisankaran, Nolan Miller, David Molitor, Heidi Williams, and participants at the 2014 American Economic
Association meetings, the 2015 American Health Economics Conference, the 2014 ASHEcon meeting, Harvard
Medical School, Harvard Law School, the Indiana University Health Economics Workshop, the NBER Joint
Healthcare and Insurance Program meeting, the NBER Health Economics Program meeting, the Pritzker School of
Medicine, the University of Chicago Applications workshop, the University of Chicago Health Economics Workshop,
the University of Illinois CBPP seminar series, UCSB, UIC, and USC for helpful comments. Charles Zhang provided
outstanding research assistance.
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I. INTRODUCTION Economists traditionally measure the benefit of a medical innovation as the improvement in health it
produces in a person who is already sick (Drummond, Sculpher et al. 2005, Murphy and Topel 2006).
Likewise, economists measure the benefit of healthcare insurance by valuing the reduction in financial
risk associated with lower out‐of‐pocket spending for medical care (Finkelstein and McKnight 2008,
Abaluck and Gruber 2011, Engelhardt and Gruber 2011). Studying either innovation or insurance in
isolation, however, overlooks fundamental connections between them. As a result, the true economic
benefit of medical technology has been inaccurately characterized and measured.
It is certainly true that a medical technology can improve the health of the sick, and that it can raise
financial risk for the healthy by imposing the burden of paying for expensive medical technologies in the
event of illness. But it also does two other things that affect its value. First, a technology can reduce
physical risk for healthy consumers who might get sick.1 New treatments make illness less unpleasant
and thus effectively raise utility in the bad state of the world, just like standard insurance contracts.
Failure to account for this feature understates the value of medical technology, particularly when it
comes to treating the most severe illnesses in the most risk‐averse consumers. Second, medical
technology does not merely create financial risk. Rather, it expands insurance possibilities by converting
a previously uninsurable physical risk into a potentially insurable financial risk.
We present a framework for valuing a morbidity‐reducing medical innovation that brings together all
these benefits and costs. To illustrate our key points, consider a healthy consumer facing the risk of
developing Parkinson’s disease,2 a neurological disorder that reduces patients’ quality of life. As is the
convention in health economics, we measure the quality of a life‐year as a proportion of a year spent in
a perfectly healthy state. For instance, a severely ill person might derive 10% of the value from one year
of life that a perfectly healthy person would, while a fairly healthy person might derive 90% of this value.
Using this construct, Parkinson’s might reduce quality of life from, say, 80% of a perfectly healthy year to
40%.3 If a perfectly healthy life‐year is worth $50,000, Parkinson’s imposes a cost of $20,000 per year
( 80% 40% $50,000). Imagine a new medical treatment that costs roughly $5,000 per year and
increases quality of life for Parkinson’s patients from 40% to 70%. This increase in quality of life is worth
$15,000 annually 70% 40% $50,000) to patients with Parkinson’s but costs only $5,000 annually. The traditional approach in health economics compares the benefit of $15,000 to the cost of
$5,000, and computes the net value of the treatment as $10,000.
This calculation neglects, however, the way the medical treatment’s introduction also compresses the
variance in the quality of life between the Parkinson’s and non‐Parkinson’s states. Prior to the
1 Our paper focuses on medical innovations that reduce morbidity and their relationship to healthcare insurance
markets. See Lakdawalla, Reif et al. (2016) for an economic analysis of mortality‐reducing innovations, which are
related to annuity insurance markets. Both these types of innovation are important, although Murphy and Topel
(2006) estimate that the historical reduction in morbidity is more valuable than the accompanying reduction in
mortality.
2 Parkinson’s disease is a progressive disorder of the nervous system that degrades a patient’s movements. It
typically manifests as a hand tremor but can also cause slowing of movement and slurring of speech, and later
dementia. Its most famous patient is the boxer Muhammad Ali. Parkinson’s symptoms can now be treated with
medications such as Levodopa or MAO‐B inhibitors that raise the level of dopamine in the brain.
3 To be clear, the numbers on the impact of Parkinson’s on quality of life in this example are made up.
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availability of treatment, the risk of Parkinson’s represented a gamble that could lower quality of life by
40% of a perfectly healthy year, or about $20,000. The treatment transforms this risk into a new gamble
that could lower quality of life by just $5,000. This reduction in the variance of quality of life outcomes
generates value for consumers who dislike risk. Of course, this risk‐reduction value is mitigated by the
arrival of a new risk, namely the potential $5,000 per year expenditure. However, if the treatment is
priced to generate consumer surplus, the ex post improvement in health outcomes will outweigh its
financial cost. For instance, prior to the development of treatment, Parkinson’s imposes a risk of losing
$20,000 in reduced health. After its development, the risk of disease is transformed into a $5,000
financial risk plus a $5,000 health risk. The new medical treatment cut the total risk of Parkinson’s in
half. Furthermore, the new financial risk created by the treatment can be mitigated or even eliminated
by healthcare insurance.
We conduct a stylized empirical exercise to explore the practical relevance of these insights. We
calculate the extent to which conventional economic studies such as Murphy and Topel (2006) have
underestimated the benefit of new medical technologies by ignoring their insurance value. The physical
insurance value associated with aggregate quality‐of‐life improvements over the past 50 years may add
as much as 50 percent to the conventional value of quality‐of‐life improvements, depending on how
those gains are distributed throughout the population. Our calculations also suggest that the physical
insurance value offered by new technologies greatly exceeds the financial spending risks that these
technologies pose and that health insurance ameliorates.
Our theoretical framework clarifies the relationship between the value of medical innovation and of
healthcare insurance. First, our model implies that medical technology itself acts as insurance. Even if a
consumer has no healthcare insurance, technology can reduce the physical risk she faces. In the
Parkinson’s example, she faced a health risk of $20,000 prior to the technology but just a $10,000 risk
after it, even if no healthcare insurance is available. This insight has important implications for health
policy. For example, providing consumers with access to better medical technology by encouraging
medical innovation may reduce risk more efficiently than providing them with healthcare insurance.
Second, our framework provides insights into the economic relationship between healthcare insurance
and medical technology. The existing literature has argued that these two products are complements by
showing that the provision of healthcare insurance can drive medical technology (Goddeeris 1984,
Newhouse 1992).4 Our approach highlights the possibility of reverse causality. Medical technology
converts a physical risk (sickness) into a financial risk (payment for treatment) that can be mitigated by
healthcare insurance. Thus, medical technology, by making healthcare insurance more useful for
smoothing health‐related risk, generates demand for healthcare (and more generally, income) insurance
(Weisbrod 1991).
Third, our framework allows economists to incorporate risk‐reduction into existing estimates of the
value from medical technology. This correction has the greatest empirical impact on treatments for
4 In general, healthcare insurance is treated as an outward shift in the demand for medical technology (Acemoglu
et al. 2006, Blume‐Kohout and Sood 2008, Clemens 2013). However, Malani and Philipson (2011) observe that
healthcare insurance can reduce the supply of human subjects for the clinical trials required for medical
innovation. Lakdawalla and Sood (2013) demonstrate that healthcare insurance and medical innovation are
complementary in the sense that healthcare insurance reduces the static inefficiency from patents and thus
reduces the cost of using patents to encourage innovation.
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severe diseases, where risks to consumers are greatest. This insight reconciles the conventional
economic approach to valuation with the findings of population surveys suggesting that people prefer to
allocate resources to treating severe diseases rather than milder ones, even holding fixed the cost‐
effectiveness of treatment across the two types of diseases (Nord, Richardson et al. 1995, Green and
Gerard 2009, Linley and Hughes 2013). Conventional approaches are hard‐pressed to account for this
finding.
Our paper unites two large literatures. The first, which estimates the consumer surplus value of health
and longevity, has found that advances in medical technology generate enormous value for consumers
(Shepard and Zeckhauser 1984, Rosen 1988, Murphy and Topel 2006). Because these studies all operate
within riskless environments, their estimates do not reflect any potential benefits accruing from risk
reduction. A second, more recent literature has documented that healthcare insurance delivers
significant value to consumers (Engelhardt and Gruber 2011, Verguet, Laxminarayan et al. 2014,
Barcellos and Jacobson 2015). This is an important finding because it justifies the cost of public
healthcare insurance programs, even if they do not generate significant increases in overall health as
several studies have found (Finkelstein and McKnight 2008, Baicker, Taubman et al. 2013). The
framework used in these studies, however, is unable to compare the value of financial healthcare
insurance to the value of physical insurance provided by medical technology.
Our paper is related to Philipson and Zanjani (2014), a contemporaneously written paper that, like the
present paper, notes that innovation converts non‐insurable physical health risks into insurance
financial payment risk. Unlike this paper, it uses this point to frame medical R&D expenditures as
insurance payments that help protect against physical risks, though ones that only pay off if R&D results
in new treatments. By contrast, this paper uses the same point to revise the literature’s estimate of
innovation to account for its insurance value. Our paper is also related to Hendren (2015), who
demonstrates that individuals obtain value from unemployment insurance not only as insurance against
unemployment, but also as ex ante insurance value against the risk of losing a job. He estimates that this
ex ante value comprises over 35 percent of the total value of unemployment insurance.
The remainder of this paper is organized as follows. Section II provides a model that describes the
different components of value of medical innovation that reduces morbidity in the sick state. Section III
presents the results of our empirical exercises. Section IV concludes.
II. FRAMEWORK FOR VALUING MEDICAL TREATMENTS Consider an individual who faces a health risk. We are interested in calculating the value of a new
medical technology that improves health in the sick state and is priced to generate non‐negative
consumer surplus even in the absence of healthcare insurance.5 Our baseline framework values the
technology from the third‐party payer’s perspective and therefore we equate the marginal “cost” of a
technology with its unit price. In reality, the marginal cost of producing many medical innovations lies
below its unit price. At the end of the theoretical presentation, we revisit our analysis from the social
perspective, which would focus on this lower marginal cost of production rather than price.
5 Lakdawalla, Reif et al. (2016) examine the value of technologies that increase longevity by reducing mortality in
the sick state.
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The individual derives utility from non‐health consumption and from health according to , . She is
either sick with probability , or well with probability 1 . Absent medical treatments, health is
when well and when sick. The individual is endowed with income when well and
when sick. Let denote the marginal utility of good ∈ , in state ∈ , .
We examine a medical treatment that promises an increase in health – specifically a reduction in
morbidity – of Δ in the sick state at a price of to be paid in the sick state. Our theoretical analysis will
focus on valuing marginal doses of the technology, i.e., and , because that will yield the most
intuitive expressions for the different components of value.6 Our numerical exercise, presented in the
next section, allows technologies to have discrete benefits and prices. In addition, our theoretical
approach here calculates a consumer’s ex ante willingness to pay for a new technology. In the appendix
we discuss how to value technology using certainty equivalents, a related approach.
A key assumption that we maintain throughout our paper is that consumers have positive demand for
income insurance, i.e., that the marginal utility of consumption is higher in the sick state than in the well
state ( ). This holds if one or both of the following are true: illness raises the marginal utility of
consumption, by affecting the curvature of utility directly; or illness reduces consumption in the sick
state by, for example, necessitating the purchase of medical care or reducing earnings, thereby
increasing marginal utility as a result. The first condition is sometimes referred to as “positive state
dependence.” While there is no consensus among economists as to whether consumers exhibit positive
state dependence, there is little doubt that the demand for income insurance is positive. Thus our
theoretical analysis maintains the weaker assumption about insurance demand, without imposing a
specific assumption around state dependence. We note that if this weaker assumption is violated, so
that , our results still obtain, but the sign of the value of insurance flips from positive to
negative. In this case, both medical technology and healthcare insurance exacerbate risk.
To clarify our terminology, we conceive of medical technology as providing “physical” benefits – e.g.,
health improvements – along with financial benefits and costs. Its value thus consists of the “physical
value” plus the “financial value.” As described in Table 1, each of these values can be further
decomposed into the value of: (1) changes in mean physical and financial outcomes; and (2) changes in
the variance of physical and financial outcomes. We call the sum of the mean effects the “conventional
value” of the technology, since this is what conventional economic analysis (e.g., cost‐effectiveness)
estimates.
Table 1: Elements in the value of medical technology.
Mean Variance Physical value Improvement in health outcomes Lower health outcomes risk Financial value Increase in healthcare spending Greater healthcare spending risk Full value Conventional value Insurance value Notes: Traditional cost-effectiveness analysis calculates the conventional value of medical technology. The spending risk component of insurance value is absent if the consumer has access to comprehensive healthcare insurance.
6 Allowing for endogenous investments in prevention does not affect our analysis. Consider, for example, a new
therapeutic treatment for an infectious disease, which can be prevented by avoiding infected individuals.
Assuming that prevention is chosen optimally, the envelope theorem implies that the choice of prevention level
will have no impact on the value of a new treatment on the margin.
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The variance consists of two effects, which we refer to as “physical risk” (lower health outcomes risk),
and “financial risk” (greater healthcare spending risk). We call the sum of these two variance effects the
“insurance value” of technology. This component is not accounted for by conventional health economic
analysis. If the consumer has access to full healthcare insurance, which eliminates spending risk, then it
is obvious that medical technology must have positive insurance value. Our analysis will show that the
insurance value is always positive, even when healthcare insurance is unavailable.
Before deriving our main results, we pause to note that our theoretical framework is quite general and
could be applied to any “innovation” that generates high value in a bad state. Health improvements are
a natural application because there is a broad consensus among economists that they are valuable, but
our analysis may also be enlightening for other applications outside of this context.
II.A. The conventional value of medical technology The standard approach to valuing medical technology typically proceeds by quantifying how much
patients are willing to pay for the technology in the sick state (Drummond, Sculpher et al. 2005). That
value, , is defined implicitly according to the following expression:
, Δ ,
Taking the full derivative of this expression with respect to components of technology (Δ and ) and
willingness to pay ( ) shows the ex post marginal value of technology ( ) to sick patients is:
This expression is the difference between the technology’s marginal benefit ( and its marginal
price ( , normalized by the marginal utility of income . 7 The “conventional” value of health technology, , is simply this marginal value to sick patients multiplied by the probability of being sick:
(1)
The conventional value measures what a sick person would pay for the health improvement.
The conventional approach is very often used to determine whether and to what extent third‐party
health insurers should cover the new technology. Yet, in a world with healthcare insurance, the more
salient question is the value of innovation as perceived by healthy people paying premiums or taxes that
finance insurance coverage. Unfortunately, the valuations of sick and healthy people coincide only when
consumers are risk neutral or possess first‐best indemnity insurance against health shocks.8 Neither of
these conditions seems realistic or appropriate.
7 As mentioned earlier, our theoretical analysis models the marginal value of the introduction of a new technology.
Mathematically, this means we evaluate the derivative at the point , .
8 By “indemnity insurance,” we mean contracts that pay consumers when a health shock occurs, regardless of how
much healthcare they use. In contrast, real‐world “healthcare insurance” pays consumers only when they consume
healthcare. See Section II.D. for additional discussion.
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The remainder of this section provides an alternative approach that values medical technology ex ante,
before the health state is realized, and illustrates how medical technology influences the size and nature
of health risks borne by consumers. We show how this approach relates to the conventional framework.
The “ex ante” value of technology consists of the conventional value plus “insurance value,” which
corresponds to the incremental value placed on medical technology by risk‐averse consumers. Under
risk neutrality, this insurance value component goes to zero, and the conventional approach coincides
with the ex ante value to premium‐paying consumers. Thus, in keeping with the terminology shown in
Table 1, we will decompose total value into “conventional value” ( ) and “insurance value” ( ). We
further break down insurance value into a “physical” ( ) and a “financial” ( ) component.9
“Physical” insurance value accrues to risk‐averse consumers even when they do not have any financial
healthcare insurance. It represents the value of reducing the physical risks of ill health. “Financial”
insurance value is the incremental gain to risk‐averse consumers from gaining access to financial
healthcare insurance.
We derive the total value under three different settings: “no healthcare insurance” ( ), “with
healthcare insurance” ( ), and “complete indemnity insurance” ( ).
II.B. The total value of technology in the absence of healthcare insurance We first assume consumers do not have access to healthcare insurance in order to show that technology
reduces risk even in the absence of financial healthcare insurance. The willingness to pay for a
technology under “no healthcare insurance,” , from the perspective of all consumers who face the
relevant health risk, is implicitly defined by:
, Δ 1 , , 1 ,
The marginal value in this case is given by the difference between the expected marginal benefit
( and the expected marginal price ( . Since we are taking the ex ante perspective of the
healthy consumer, we normalize by the ex ante marginal utility of income:
1
Rearranging this expression shows that the value of technology with no healthcare insurance, ,
can be expressed as the conventional value, , plus an additional component that reflects the
insurance value of the technology, :
,
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,
(2)
Insurance value in the absence of insurance, , is always positive, provided that the technology is
priced such that its conventional value is positive, and provided the individual has positive demand for
9 Using the language of Ehrlich and Becker (1972), one could call “self‐insurance value” when healthcare
insurance is absent because it measures the ability of technology alone to reduce risk, and call “market
insurance value” because it reflects the ability of financial insurance to mitigate spending risk introduced by a new
technology.
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income insurance against the health risk (i.e., ). This important result bears repeating: even
absent healthcare insurance, any medical technology that is worth purchasing ex post reduces overall
risk ex ante, because the reduction in physical risk more than offsets the increase in financial risk.
The insurance value of technology in the absence of healthcare insurance can be written explicitly as the
reduction in physical health risk minus the increase in financial risk:
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The reduction in health risk gets larger as the value of the health improvement, , gets larger. The
increase in spending risk gets larger as the technology’s price, , gets larger. Our numerical exercise
will quantify the size of these two insurance components and compare them to the conventional value.
II.C. The total value of technology with healthcare insurance Healthcare insurance mitigates the spending risk created by new technology and thus boosts the overall
insurance value created when new technologies are introduced. Consider an actuarially fair, fee‐for‐
service healthcare insurance contract that pays the consumer when she falls sick.10 When , the individual has complete fee‐for‐service (FFS) healthcare insurance; when , the individual
has incomplete FFS insurance due to, e.g., deductibles, co‐payments, annual caps, or other patient cost‐
sharing features.
In this environment, the individual solves the problem:
max , Δ 1 , subject to
In practice, most consumers are not completely insured against health risks. Therefore, the transfer
constraint will typically bind, and the consumer will choose ∗ .
Define as the total value of technology “with healthcare insurance”. Using the expression for the
optimal transfer ∗, we can implicitly define this value as:
1 , Δ 1 ,, 1 ,
The corresponding marginal value of technology with healthcare insurance ( ) is given by:
1
1
(3)
We can relate to the earlier expression for conventional value, , and insurance value without
healthcare insurance, , according to:
10 Because the contract is actuarially fair, the insurance premium is equal to . This means a consumer in the
sick state will receive a net transfer of 1 when sick.
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0 11
,
(4)
The value of technology with healthcare insurance is equal to its conventional value, plus the insurance
value that accrues without any healthcare insurance available, plus a component that reflects the
incremental value of financial healthcare insurance made possible by technology.
If healthcare insurance is complete, so that , then it will perfectly offset and eliminate the
financial risk introduced by the new technology. Mathematically, if 1, then . In this
special case, the total value of technology is equal to the conventional value plus the value of physical
risk reduction:
II.D. The total value of technology under complete indemnity healthcare insurance What happens if the consumer has access to perfect indemnity insurance, as opposed to healthcare
insurance covering only the cost of medical care? While rarely observed in practice, indemnity insurance
is frequently assumed in economic models of health for analytical convenience (e.g., Murphy and Topel
2006). Because the consumer faces no constraints on the amount of money she can transfer across
states, she will choose an amount that equalizes the marginal utility of wealth across states, even
when she does not have access to medical technology:
1, ,
Full indemnity healthcare insurance is fundamentally different from the healthcare insurance we
considered earlier, because indemnity insurance operates even in the absence of medical technology.
This means that the marginal value of a new technology is measured at the point , , not
, . We therefore denote the indemnity‐insured marginal utility of good ∈ , in state ∈, as . Because , it is straightforward to show that the value of a new medical technology
under “indemnity insurance” is equal to
Notice that this expression is substantially similar to equation (1), the expression for the conventional
value. In fact, if the marginal utilities for are calculated in the indemnity insured state, then
. In that case, the conventional value of medical technology is equal to the value in a setting where
consumers face no risk thanks to perfect indemnity insurance. In principle, some differences arise,
because conventional approaches typically fail to calculate marginal utilities in the indemnity‐insured
state. Nonetheless, the structure of the conventional value calculation is identical to that of the
indemnity insurance case. In other words, the conventional approach to valuing medical technology
coincides with the ex ante value of technology when individuals are fully insured against health shocks
by perfect indemnity insurance.
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II.E. Implications for valuing health gains If individuals are risk averse and have positive demand for income insurance—which empirical evidence
suggests is true—then our model shows that the conventional valuation of medical technology
underestimates the true value. This has important implications for cost‐effectiveness analysis, which is
widely employed by healthcare systems across the world to determine which medical treatments qualify
for insurance coverage. Moreover, economic studies such as Murphy and Topel (2006) abstract away
from the insurance value of technology and thus exclude an important source of value associated with
health improvements.11 We return to this point in our numerical exercise.
Our results also have important implications for the relative values of different types of medical
technologies. This can be seen by examining the effect of health status in the sick state, , on our
analytical expressions for the value of a marginal technology. This is of particular interest because low
values of reflect diseases with high “unmet need”, e.g., Parkinson’s disease, hepatitis C, or
amyotrophic lateral sclerosis (ALS). There is much contemporary debate concerning how much insurers
should pay to treat these diseases. Our framework suggests that both the conventional and insurance
values of medical technology may be higher for more severe diseases. Thus, the total value of a medical
technology is higher for diseases with a higher degree of unmet need (i.e., diseases associated with low
values of ). Moreover, the difference between the conventional value and the total value grows as the
degree of unmet need rises. This suggests that errors in the use of the standard approach are most likely
for severe diseases with a poor current standard of care. This prediction is consistent with stated
preference evidence that people who are sicker have higher willingness to pay for medical technology,
even when the health benefits remain constant. Survey evidence suggests that people value a given
level of health investment more highly when provided to sicker patients (Nord, Richardson et al. 1995,
Green and Gerard 2009, Linley and Hughes 2013).
To understand these arguments, differentiate equation (2) with respect to health in the sick state:
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Suppose that, as we maintain throughout the paper, there is positive demand for insurance (
0). Also assume a slightly stronger version of this assumption: 0. Then a sufficient condition for
0 is that 0 (which holds necessarily for certain classes of utility functions,
e.g., Cobb‐Douglas). Moreover, since each individual component term of also falls with , it
follows that both the conventional value and the insurance value fall with as well.
From a practical standpoint, our analytical framework can be implemented empirically with knowledge
of a few key parameters. Standard cost‐effectiveness analyses rely on estimates of the value of health
gains , the marginal health gain from the new technology , and the marginal cost of the new
11 Although consumers in Murphy and Topel (2006) have uncertain lifespans, their quality of life at any given age is
known with certainty and they have access to perfect credit markets. Thus healthcare insurance has no value in
their model.
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technology ( . The two additional parameters in our framework are the probability of illness , and
the marginal rate of substitution between the sick and well states ( / ). The probability of illness can
be estimated as the incidence of disease in the population of interest. In principle, the marginal rate of
substitution can be recovered by estimating the demand for healthcare insurance. For instance, shocks
to the loading cost of healthcare insurance can be used to trace out the marginal rate of substitution as
a function of the quantity of healthcare insurance purchased. The advantage of this approach is the use
of revealed preference to recover the quantity of interest directly. The drawback is the difficulty of
finding suitable experiments for every population of interest. An alternative would be to parameterize a
utility function and recover the implied estimates of , and , . The income in the sick
and well states could be obtained from population surveys of health and income, such as the US Medical
Expenditure Panel Survey (MEPS). The health levels could be estimated from similar sources. For
example, the MEPS measures health‐related quality of life using a five‐question instrument known as
the EuroQol five dimensions questionnaire (EQ‐5D). Quality of life is measured using this scale, which
ranges from zero to one.
The approach above took the perspective of the third‐party payer, for whom marginal cost is equal to
price. The social planner’s perspective takes marginal cost to be the marginal cost of production. In
many cases, e.g., pharmaceuticals, marginal production costs are quite small relative to prices. For
example, some estimates suggest that pharmaceutical prices are about 5 times marginal cost (Caves,
Whinston et al. 1991). From the social planner’s perspective, therefore, is relatively small, because it
reflects only the marginal cost of production. As such, the social value of technology is determined
primarily by the conventional value plus the value of physical risk‐reduction. The value of financial risk‐
reduction is much smaller.
This also raises the question of innovation incentives. The classic Nordhaus model (Nordhaus 1969)
implies that the social value of the technology should optimally be equal to innovator profits. “Patent
race” models (Loury 1979) and other alternative models take issue with this result, although none of
them provides a clear prediction on how to relate profits to value. Under the simpler Nordhaus
formulation, our theory predicts that rewards for innovation should rise with higher insurance value.
Our theoretical analysis focused on technologies that treat disease, because the distinction between ex
post and ex ante valuation is most relevant here. Technologies that prevent disease are always assessed
from the ex ante standpoint of healthy people. A subtler issue arises with treatment technologies that
affect incentives for preventive behavior. For example, a new treatment for an infectious disease might
affect incentives to prevent infection. In this case, however, the behavioral response is second‐order to
the introduction of the treatment technology. Thus it has no first‐order welfare consequences and does
not affect the value of the treatment technology on the margin. It may, however, have some
inframarginal value that could be considered in special cases like that of infectious diseases where
behavior substantially affects risk.
III. ILLUSTRATING THE VALUE OF MEDICAL INNOVATION There is substantial evidence that the average quality of life has improved dramatically over the past
fifty years. The proportion of elderly who are disabled has decreased, and the proportion who are active
has increased (Cutler 2005). Previous work has estimated that the increase in quality of life may be more
valuable than the accompanying increase in life expectancy between 1970 to 2000, which itself is valued
at roughly $95 trillion (Murphy and Topel 2006). We conduct a numerical exercise to understand how
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Murphy and Topel’s estimated value from improvements in quality of life might change when one
accounts for the insurance value of medical innovation.
Because data on the marginal costs of medical technologies to consumers (i.e., prices) or to producers
(including the cost of innovation and manufacturing) are generally unavailable, our value estimates
account only for consumer surplus and assume prices are a fixed percentage of the willingness to pay for
health improvements. Focusing on consumer surplus does not affect the policy implications of our
findings: most health technology assessment agencies ignore producer surplus in their calculations (Jena
and Philipson 2008), and our estimates of the relative importance of the insurance value of medical
innovation are not sensitive to reasonable changes in the price of technology.
We assume that utility is additively separable in consumption and health, and that it takes a CRRA form:
,1
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1
The theoretical model presented in the first half of this paper allowed for only one possible sick state.
Here we employ a generalized version that allows for an arbitrary number of sick states. The health
status and probability of a particular state are given by and , respectively. A medical technology
can improve the health of any state by an amount Δ for price .
The proper value of risk aversion among real‐world populations remains controversial, with estimates
ranging from less than 1 to more than 10.12 We adopt 2 as our preferred estimate. Employing a
larger (smaller) value would increase (decrease) our estimates of insurance value.13
We assume throughout that income in the well state, , is equal to $120,000, which is approximately
the value of full income for a typical individual (Murphy and Topel 2006). Full income here embeds all
sources of non‐health consumption, including leisure. We assume that income decreases by 20 percent
in the sick state ( 0.8 , which incorporates the documented empirical finding that poor health
tends to decrease income (Smith 1999).
Our numerical exercise requires us to measure health in some manner. We pursue this in a manner
consistent with the prior literature. We estimate the lifetime benefits of an increase in quality of life, ∆ ,
similar to the measure considered in Murphy and Topel (2006), using data from a nationally
representative sample of individuals from the Medical Expenditure Panel Survey (MEPS). We follow
Philipson and Jena (2006), who find that average prices for medical technology are about 20% of ex post
willingness to pay plus producer surplus. Assuming that producer surplus is roughly equal to price, since
production costs are quite small, this would imply that price is roughly 25% of ex post consumer surplus.
We report all estimates of insurance value from an ex ante perspective. Thus, they should be regarded
as the values accruing to an individual who is facing a risk of illness rather than to an individual who is
already ill. The appendix provides details on how we implement our calculations, and also generalizes
our main model to accommodate an arbitrary number of sick states.
12 A less than comprehensive list includes Barsky et al. (1997), Chetty (2006), Cohen and Einav (2005), Kocherlakota
(1996), and Mehra and Prescott (1985).
13 Employing a larger value of also increases our estimate of the conventional value, but by less than the increase
in insurance value.
13
Our numerical exercise estimates the conventional and insurance values of technology. We also
decompose insurance value into its two subcomponents: physical insurance value and financial spending
risk (see Table 1). Absent healthcare insurance, the total value of technology is equal to the sum of
conventional value, physical insurance value, and the offsetting financial spending risk. If complete fee‐
for‐service healthcare insurance is available, financial spending risk is equal to 0 and the total value of
technology is then equal to the conventional value plus physical insurance value.
Let represent the distribution of health risks. We measure as “quality of life,” employing a
widely used and well‐validated tool for measuring quality of life known as the EQ‐5D (or EQ‐5D‐3L). The
EQ‐5D measures quality of life on a scale from zero to one, using answers from five survey questions
regarding the extent of the respondent’s problems in mobility, self‐care, daily activities, pain, and
anxiety/depression. All these questions are asked of respondents in the 2000‐2003 MEPS, which serves
as our host database.
We use the EQ‐5D measure to estimate baseline health state status by age group and gender. The
measure is summarized in Table 2 for every 10th percentile. The table shows that the 10th percentile of
health status for 18‐34‐year‐old males corresponds to an EQ‐5D score of 0.726. For each quantile, health
status declines with age, as expected. Conditional on age, males are estimated to have a higher quality
of life than females. In every group, the 90th percentile enjoys perfect health. In our analysis, we assume
that each health status displayed in Table 2 represents health status in an untreated sick state, . For
each gender and age group, there are nine possible states, each occurring with probability 1/9. Throughout our analysis, we conceive of the health state as a percentage of perfect health, consistent
with the literature on quality‐adjusted life‐years. However, the numerical calculations require us to
choose some absolute scale for health. For convenience, we rescale it to range from 0 to 120,000, so
that health and consumption are scaled similarly.
Next, we estimate how much a consumer facing the health risk distribution described in Table 2 would
be willing to pay, ex ante, for a hypothetical average increase in her quality of life. We assume an
average increase in the quality of life of 6,000 (or five percent of perfect health), and concentrate all of
the gain in the two poorest health states. This average health increase is in line with the hypothetical
increase considered by Murphy and Topel (2006).14
Our results are displayed in Table 3. They show that the total annual value of the health increase is equal
to $1,575 for males between the ages of 18 and 34. This total can be broken down into $1,386 of
conventional value and $189 (=$217‐$28) of insurance value. Both the conventional and insurance
values increase with age because the elderly are less healthy and thus have more to gain from health
improvements. Young individuals, by contrast, already have a high probability of enjoying perfect health,
which cannot be improved. The conventional value is responsible for the bulk of the health gain when
individuals are young, but the fraction of the gain due to insurance increases steadily with age. For the
oldest age groups, the insurance value of the health gains significantly exceeds the conventional value.
This is due to the large dispersion in health states for the elderly, as shown in Table 2. Because the
elderly face the most health risk, they enjoy the highest insurance value from an increase in the quality
of life.
14 Murphy and Topel (2006) assume that advances in quality of life are related to the declines in mortality from
1970‐2000. Life expectancy for 18‐year‐olds increased by about 5 percent during that period.
14
We calculate the aggregate per capita lifetime value of these health gains for an 18‐year‐old by
aggregating over age groups. We discount our calculations by the probability of survival and by a real
rate of discount equal to three percent.15 The results, displayed in Table 4, show that the hypothetical
health increase we consider generates about $60,000 and $80,000 in conventional value for an 18‐year‐
old male and female, respectively.
We also compute that the insurance value adds 38 to 62 percent to the conventional value, as shown in
the last column of Table 4. This suggests that the value of advances in the quality of life may be
significantly higher than has previously been recognized. The results from Table 3 also suggest that the
magnitude depends greatly on how those gains were distributed across the population.16 The value is
greatest if it accrues to the oldest and sickest individuals (those with a high degree of “unmet need”),
and lowest if it accrues to those who were already relatively healthy. This reflects our earlier theoretical
result that the difference between the conventional value and the total value of health gains grows with
the degree of unmet need. To date, relatively little attention has been paid to the distribution of
historical health gains, and how it influences the total social value of those gains.
Finally, we note that the physical insurance values reported in Table 4 greatly exceed the financial
spending risks. Prior studies have argued that healthcare insurance programs provide enormous value
by reducing financial spending risk (Finkelstein and McKnight 2008, Engelhardt and Gruber 2011,
Barcellos and Jacobson 2015). Our numerical exercise suggests that implementing policies to encourage
medical innovation may generate even greater insurance value than expanding access to healthcare
insurance.
IV. CONCLUSION When real‐world healthcare insurance markets are imperfect, risk‐averse consumers derive value from
medical technologies that limit the consequences of bad events and expand the reach of financial
healthcare insurance.
Our numerical exercise suggests that these theoretical observations are empirically meaningful. New
medical technologies provide substantial insurance value above and beyond standard consumer surplus.
Under plausible assumptions, the insurance value adds about 50 percent to the conventional value.
Notably, the physical insurance value of technology is generally much larger than the financial insurance
value created by healthcare insurance. The latter point suggests that medical technology on its own may
do more to reduce risk than healthcare insurance.
Our argument also suggests that the academic literature, which tends to focus exclusively on the
standard consumer surplus value of medical technology, may have failed to capture a significant portion
of its value. For example, Murphy and Topel (2006) value health increases over the past century at over
15 Survival probabilities are obtained from www.mortality.org. Discount rates are calculated for the midpoint of the
age group. For example, the expected conventional value for an 18‐year‐old male for the period covering ages 18‐
34 is equal to $1,479 17 0.99886/ 1 0.03 / , where the first term comes from Table 3, 17 34 181, the third term is the probability of surviving from age 18 to age 35, and the last term is the discount rate.
16 Like most insurance studies, we implicitly assume that health shocks are uncorrelated over time. Relaxing this
assumption would increase the value of insurance because correlated shocks imply even greater physical risk
(Kowalski 2015).
15
$1 million per person. Our results suggest that accounting for insurance value could significantly
increase their estimates.
The ability of medical innovation to function as an insurance device influences not just the level of value,
but also the relative value of alternative medical technologies. The conventional framework understates
the value of technologies that treat the most severe illnesses, compared to technologies that treat mild
ailments. This helps explain why health technology access decisions driven by cost‐effectiveness
considerations alone often seem at odds with public opinion. For example, survey evidence suggests
that representative respondents evaluating equally “cost‐effective” technologies strictly prefer paying
for the one that treats the most severe illness (Nord, Richardson et al. 1995).
From a normative point of view, our analysis also implies that the rate of innovation functions in a
manner similar to policies or market forces that complete or improve the efficiency of insurance
markets. Increases in the pace of medical innovation reduce overall physical risks to health, and thus
function in a manner similar to expansions in healthcare insurance. As a result, policymakers concerned
about improving the management of health risks should view the pace of medical innovation as an
important lever to use in their efforts. US policymakers have focused their efforts on improving
healthcare insurance access and design. While these are worthy goals, medical innovation policy may
have an even greater impact on reducing risks associated with bad health shocks.
More practically, our analysis informs the contemporary debate over how new medical technologies
should be reimbursed. The United Kingdom provides an instructive example, as the UK health
authorities hew closely to the use of ex post consumer surplus as a measure of value for a new
technology, and thus a guide to how generously it should be reimbursed. Perhaps as a result, the UK
performs poorly in the reimbursement of drugs to treat cancer, which has motivated legislators there to
provide exceptional reimbursement for such products, above and beyond what the UK health
authorities dictate (Lancet, 2010). Controversy has erupted over the appropriateness of this approach,
and the legislation has drawn a great deal of criticism (Lancet, 2010). Yet, our analysis illuminates how
the severe nature of cancer might contribute to the major misalignment between the standard
economic approach to valuing medical technology and the preferences of legislators and voters. The
policy lesson is that more attention needs to be paid by third‐party payers and other health
policymakers to covering treatments for severe diseases in order to align payment policies with the
values of consumers. Moreover, the standard economic approach to valuing health technology should
itself work towards alignment with the preferences of healthy consumers and sick patients.
16
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19
APPENDIX
A. Accommodating multiple sick states The model presented in the main text allowed for two health states, one sick and one well. Here we
generalize the model to allow for an arbitrary number of sick states. Let the probability of each sick state
be , where 1… . Define the probability of the well state as 1 1 ∑ . Suppose that,
for each sick state, there is a medical technology available that increases health by an amount Δ for a
price . The conventional value is equal to
where each is defined implicitly as
/ , ,
The full ex ante willingness to pay for a technology under “no healthcare insurance” is defined implicitly
as
, Δ 1 ,
where , expected utility absent medical technology, is defined as
, 1 ,
The ex ante willingness to pay “with healthcare insurance” is implicitly defined as
, Δ 1 ,
When 1, we have 1 1 and all of the above expressions simplify to the two‐state case
presented in the main text.
We solve for , , and using standard numerical methods. The insurance value is equal to the
incremental willingness to pay when accounting for risk: . Financial spending risk is equal
to the incremental willingness to pay when an individual gains access to financial insurance markets:
. The physical insurance value can then be easily computed as .
B. Employing certainty equivalents Define a certainty equivalent as the maximum amount that a consumer is willing to pay to completely
insure against risk. For an individual without access to medical technology or financial insurance
markets, the certainty equivalent, , is defined implicitly as:
, , 1 ,
20
Following the introduction of a new medical technology that generates positive consumer surplus, the
certainty equivalent, , is defined implicitly as:
, , Δ 1 ,
The new medical technology reduces the certainty equivalent for two distinct reasons. First, the new
technology generates consumer surplus for sick individuals. This is what we call the “conventional value”
of technology. Second, the technology generates what we call “insurance value” because the consumer
now faces less risk. Note that the first source of value comes from a reduction in the mean and the
second comes from a reduction in the variance.
Finally, consider the case where the consumer has access to fee‐for‐service healthcare insurance. The
certainty equivalent, , is now defined implicitly as:
, 1 , Δ 1 ,
The conventional value ( ), net insurance value ( ) and financial spending risk ( ) associated with a
new technology are equal to the incremental reductions in uncertainty associated with the introduction
of the technology and the availability of health care insurance:
The physical insurance value can then be defined as . A shortcoming of employing
certainty equivalents is that it does not separately identify (a mean shift) and (a variance shift).
This is not a problem for most studies that value insurance because the mean shifts are typically already
measured in dollars. For example, Finkelstein and McKnight (2008) subtract out changes in mean
medical spending following the introduction of Medicare so that their welfare estimates can be
attributed solely to risk reduction. We cannot do that in our setting because changes in health, unlike
changes in medical spending, are not measured in dollars.
One might be tempted to estimate using the willingness to pay method we present in the main text.
Doing so can generate nonsensical estimates, however, because willingness to pay is calculated from the
perspective of the sick state while certainty equivalents are always calculated from the healthy state,
and those states employ different marginal utilities of income. For example, it is possible to generate
scenarios where the insurance value is negative even though a consumer has positive demand for
income insurance in the sick state. Nevertheless, we obtain similar results overall if we estimate our
model using certainty equivalents rather than the willingness to pay method we present in the main
text.
21
TABLES
Table 2. Average health status for selected quantiles, by age group and gender.
Table 3. Value of a modest health improvement that is concentrated in the two lowest health states.
Group Observations 10 20 30 40 50 60 70 80 90
Males (18‐34) 11,382 0.726 0.796 0.886 1 1 1 1 1 1
Males (35‐49) 11,424 0.681 0.743 0.796 0.835 1 1 1 1 1
Males (50‐64) 7,998 0.62 0.691 0.74 0.796 0.796 1 1 1 1
Males (65‐79) 4,344 0.569 0.681 0.704 0.727 0.796 0.796 0.962 1 1
Males (80+) 1,120 0.208 0.56 0.638 0.699 0.725 0.761 0.796 0.916 1
Females (18‐34) 13,049 0.717 0.787 0.835 0.895 1 1 1 1 1
Females (35‐49) 13,351 0.62 0.725 0.787 0.8 0.857 1 1 1 1
Females (50‐64) 9,210 0.534 0.689 0.725 0.761 0.796 0.826 1 1 1
Females (65‐79) 5,567 0.332 0.62 0.691 0.721 0.743 0.796 0.814 0.971 1
Females (80+) 2,077 0.116 0.427 0.62 0.681 0.696 0.731 0.796 0.844 1
Notes: Table presents pooled, weighted estimates from the 2000‐2003 MEPS. Each cell
represents the average EQ‐5D index for that quantile and group. The EQ‐5D index is a
measure of quality of life that ranges from 0 (poor health) to 1 (perfect health).
Quantiles
Group Conventional Physical insurance Financial spending risk Total
Males (18‐34) $1,386 $217 $28 $1,575
Males (35‐49) $1,950 $393 $45 $2,299
Males (50‐64) $2,629 $683 $69 $3,243
Males (65‐79) $3,461 $1,186 $106 $4,541
Males (80+) $7,421 $10,128 $525 $17,024
Females (18‐34) $1,785 $336 $39 $2,081
Females (35‐49) $2,541 $647 $66 $3,122
Females (50‐64) $3,355 $1,143 $102 $4,396
Females (65‐79) $5,592 $4,084 $269 $9,408
Females (80+) $9,494 $22,420 $1,034 $30,880
Notes: This table displays the annual value of a modest hypothetical increase in quality of life that is
concentrated in the two poorest health states, for an individual facing the health risk profile displayed in
Table 2. The total value is equal to the conventional value plus the physical insurance value minus the
financial spending risk.
Insurance value
22
Table 4. Aggregate lifetime value of the health improvement from Table 3.
Gender Conventional Physical insurance Financial spending risk Total Value added by insurance
Male $61,915 $25,378 $1,957 $85,336 38%
Female $84,582 $55,796 $3,578 $136,800 62%
Notes: Estimates are weighted to reflect discounting and survival probabilities. The total value is equal to
the conventional value plus the physical insurance value minus the financial spending risk.
Insurance value